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If x varies directly as y and x = 10 when y = 2, find x when y = 7.
25
30
35
40
35
Observe that y doubles to 4, then triples to 6... or simply note that x is always 5 times y (10/2=5). Thus, when y = 7, x = 7 * 5 = 35.
x varies directly as y, where x = 10 when y = 2.
y1тАЛx1тАЛтАЛ=y2тАЛx2тАЛтАЛ
Observe that y doubles to 4, then triples to 6... or simply note that x is always 5 times y (10/2=5). Thus, when y = 7, x = 7 * 5 = 35.
Students often accidentally set up an inverse proportion (x1тАЛтЛЕy1тАЛ=x2тАЛтЛЕy2тАЛ) instead of direct proportion, leading to an incorrect result of 2.85.
Define the relationship
Since x varies directly as y, the ratio of x to y is constant (k).
k=yxтАЛ=210тАЛ=5
Set up the equation for the new value
Using the constant k=5, we set up the equation for y=7.
x=k├Чy
Calculate the result
Substitute the values into the equation: x=5├Ч7.
x=35
C is correct because multiplying the constant ratio of 5 by the new value of y=7 yields 35.
Direct variation is the fundamental concept behind unit pricing and percentage calculations; if you understand this, you can solve most profit/loss proportionality problems quickly.
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